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Chapter 6: Problem 18

Solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$a=4, b=6, c=9$$

Short Answer

Expert verified
The respective angles for lengths a, b, c are 伪, 尾, 纬 degrees, rounded to the nearest degree.

Step by step solution

01

Find Angle 纬

We first apply Law of Cosines to find the angle 纬: \(9^2 = 4^2 + 6^2 - 2 \cdot 4 \cdot 6 \cdot \cos(纬)\). After re-arranging, we'll get \(\cos(纬) = (4^2 + 6^2 - 9^2) / (2 \cdot 4 \cdot 6)\). 纬 is then the arccos of this value.
02

Find Angle 尾

We then use Law of Sines to find 尾: \(\sin(尾) / 6 = \sin(纬) / 9\), implies after re-arranging, we'll get \(\sin(尾) = sin(纬) / 9 * 6\). 尾 is then the arcsin of this value.
03

Find Angle 伪

Finally, knowing that the angles in any triangle sum to 180 degrees, we can find 伪 as \(伪 = 180 - 纬 - 尾\)

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